Published on 04/11/2011

#### Activity Overview

This lesson involves finding the area under the standard normal curve with mean 0 and standard deviation 1 for a given distance from the mean and compare this to the area under the curve for another member of the family of normal curves.

#### Objectives

- Students will identify the percent of area under any normal curve that is 1, 2, or 3 standard deviation units from the mean.
- Students will recognize that for any member of the family of normal curves, the areas whose boundaries are the same number of standard deviations from the respective means of the curves are always equal.

#### Vocabulary

• z-score

• probability density function

• mean

• symmetry

• standard deviation

• standard normal curve

#### About the Lesson

This lesson involves finding the area under the standard normal curve with mean 0 and standard deviation 1 for a given distance from the mean and compare this to the area under the curve for another member of the family of normal curves.

As a result, students will:

- Play a Match the Area game, and learn that the areas 1, 2, and 3 standard deviations from the mean are approximately 68%, 95%, and 99.7%, respectively, of the total area under the curve regardless of which normal curve is being examined (the empirical rule).
- Change the mean and standard deviation to learn that the area between the boundaries determined by any given distance from the mean, when measured in standard deviation units, is equal for any member of the family of normal curves.